Quantum Tanner Codes at Moderate Blocklength

Feroz Ahmed Mian; Vaishnavi L. Addala; Arman Meraj; Adhiraj Chadha; Stefan Krastanov

Quantum Tanner Codes at Moderate Blocklength

量子物理 2026-08-12 v1

作者: Feroz Ahmed Mian , Vaishnavi L. Addala , Arman Meraj , Adhiraj Chadha , Stefan Krastanov

摘要

We present explicit constructions of quantum Tanner (QT) codes with good rate and distance, obtained through two complementary approaches: the left-right Cayley complex (LRCC) description and the "lifting" perspective, in which a seed Calderbank-Shor-Steane (CSS) code is lifted by commuting left-right regular actions of a finite group $\mathcal{G}$ . Through an extensive search over non-abelian groups from GAP's SmallGrp library, we investigate the moderate-blocklength regime ( $n \in [500,1000]$ ) and identify several new code instances with distance upper bounds exceeding $20$ . These include $[[480,8,(\leq 21,\leq 21)]]$ , $[[504,4,(\leq 36,\leq 27)]]$ , $[[672,4,(\leq 48,\leq 28)]]$ , $[[720,6,(\leq 30,\leq 30)]]$ , and $[[864,8,(\leq 39,\leq 31)]]$ , with these bounds obtained using up to $350$ million trials of sQetch, a randomized distance estimator. The code instances presented have check weights ranging from $9$ to $20$ . Using the Tesseract decoder, we estimate pseudo-thresholds of $3.6\%$ - $4.6\%$ under phenomenological noise and $0.14\%$ - $0.27\%$ under circuit-level noise, comparable to prior results at shorter code lengths. We also provide QuantumExpanders.jl, an open-source Julia library for constructing QT codes and explicit constructions of Ramanujan graphs.

引用

@article{arxiv.2608.12509,
  title  = {Quantum Tanner Codes at Moderate Blocklength},
  author = {Feroz Ahmed Mian and Vaishnavi L. Addala and Arman Meraj and Adhiraj Chadha and Stefan Krastanov},
  journal= {arXiv preprint arXiv:2608.12509},
  year   = {2026}
}